Random Sampling and Sampling Methods
Random Sampling and Sampling MethodsRicky Singh 13/0939/2052Gary Westford 14/0939/2054Christopher Blackman 13/0939/2477Geetendra Singh 13/0939/2428Dustin Roache 14/0939/2115Outline of PresentationObjectiveDefinition of Key TermsIntroductionSamplingReasons for SamplingForms of SamplingRandom Sampling and Sampling MethodsOther Sampling MethodsErrors of Sampling Reasons for Sampling ErrorsSummaryConclusionReferencesObjectiveBy the end of this lesson, students should be able to:Identify and describe different Sampling Methods
Apply the different methods to any given situationDefinition of Key TermsPopulation (N) the total set of observations to be made or the larger set of objects to be studied.
e.g. a stockpile of aggregates
Sample (n) a set of observations drawn from a population or a set of representative objects we choose in order to estimate the characteristics of the larger set of objects.
e.g. the portion of the stockpile that passes through the No. 4 Sieve.Parameter a measurable characteristic of a population, such as a mean or standard deviation
Statistic a measurable characteristic of a sample, such as a mean or standard deviation.
Random Number a number determined totally by chance, with no predictable relationship to any other number
Sampling Unit the potential member of a sample i.e. the subject under observation on which information is collected.
Sampling Frame the set of sampling units from which the sample will be drawn i.e. the list of all the sampling units from which the sample is drawn. Summary of Sampling TermsPopulationSampleSampling UnitIntroductionIn conducting a research, it is important that a sample of subjects:
Can be studied at an acceptable cost in time and money
Is large enough to control random error in generalizing the study findings to the population
Is representative enough to control systematic error in these inferences.SamplingSampling is the process of selecting a small number of elements from a larger defined group of elements such that the information gathered from the small group will allow judgments to be made about the larger group.
Reasons for SamplingSampling is done to obtain information from large populations with:
Reduced field time
Reduced costs
Increased accuracy with enhanced methods
Reasons for SamplingSampling error could be estimated
Sometimes studying the whole population is impossible
Forms of SamplingThere are two main forms of sampling:
Probability Sampling uses a random process to guarantee that each unit of the population has a specified chance of selection.
Non-probability Sampling a sampling method in which the probability that a unit is selected is unknown i.e. the total population number or denominator is unknown.Random Sampling and Sampling MethodsRandom Sampling is a type of Probability Sampling
It is a method of randomly selecting sample(s) of data to help solve a problem on the whole data.
In this method, each member of the population has an equal chance of being selected.Random Sampling MethodsThere are five (5) different Random Sampling Methods:
Simple Random Sampling
Stratified Random Sampling
Cluster Sampling
Systematic Sampling
Multi-Stage Sampling
Simple Random SamplingSimple Random Sampling has the following properties:
The population consists of N objectsThe sample consists of n objectsAll possible samples of n objects are equally likely to occur
This method is best suited where not much information is available about the population, the population is widely dispersed and less emphasis is placed on efficiency.
Simple Random Sampling ContdThis technique can be conducted using the lottery method.
However, it is recommended that a table of random numbers or a computer generated list of random numbers be used.
Simple Random Sampling Contd14318515961022211242071721131912251423816A Random Numbers TableSimple Random Sampling Contd
Table 1: Correct Method of Using A Random Numbers TableTable 2: Incorrect Method of Using A Random Numbers TableTypes of Simple Random SamplingThere are two (2) types of Simple Random Sampling:
Replacement Sampling a sample unit is selected and then replaced before the next sample is selected.
Non-replacement Sampling the sample unit is not replaced after it has been selected.Procedure for Simple Random SamplingDetermine sample size, n.Select sample units either by the lottery method or the table of random numbers.Determine the type of simple random sampling.Calculate the probability Example Replacement SamplingA surveyor is conducting an audit of the accuracy of all the theodolites, within his warehouse, used to conduct surveys within the last month.
He randomly selects ten (10) theodolites (n) out of the total one hundred (100) theodolites (N) to be tested for correct calibration.
The first theodolite is selected and its calibration crossed checked and replaced.
Example Replacement Sampling ContdThe probability, P1, of randomly selecting the first theodolite is 1/10.
When the theodolite is returned to the sampling frame and another theodolite is drawn, the probability P2 of selecting the second theodolite will also be 1/10 since the number of theodolite in the sampling frame is 10 due the first theodolite which was tested being replaced. P1=P2.
Example Non-Replacement SamplingIn non-replacement sampling, each theodolite will not be returned to the sampling unit after being tested.
Therefore, P1 = 1/10
Hence, the second theodolite will have a probability P2 = 1/9 and P1 is not equal to P2Simple Random Sampling SummaryTwo types Replacement Sampling and Non-Replacement Sampling.
Probability calculation:Replacement:Pr =
Non-Replacement:Pr =
WherePr is the probability for a given turnn is the sample numberr is the turn number
Stratified Random SamplingThe population consists of N elements
The population is divided into H groups, called strata
Each element of the population can be assigned to one, and only one, stratum.
Stratified Random Sampling ContdWithin each strata, a probability sample is selected (often a simple random sample).
The ratio of each stratum sample size to the total sample size must be the same as that of its stratum size to the population size.Example Stratified Random SamplingThe Public Relations Department of the GWI would like to survey its customers to obtain the opinions of the residents of the quality of the service being provided.
It is decided that 90 residents from the twelve (12) District Meter Areas (DMA) in Georgetown will be interviewed, of which 8 have Water Treatment Plants and 4 are without.
Example Stratified Random SamplingThe PR Officer must first calculate the numbers of residents of each type of DMA he should interview.
Therefore, the selection process is as follows:
Residents of the Water Treated Areas: 8 x 90 = 60 12Residents of the Areas not treated: 4 x 90 = 30 12 Advantages of Stratified Random SamplingProvides greater precision
It requires a smaller sample, which saves money
Guards against an unrepresentative sample.
Can support a separate analysis of any subgroup.Disadvantage of Stratified Random SamplingIt may require more administrative effort than a simple random sample. Cluster SamplingThe population is divided into N groups, called clusters.
The researcher randomly selects n clusters to include in the sample.
Each element of the population can be assigned to one, and only one, cluster.
Cluster SamplingVery useful when the population is widely dispersed and it is impractical or costly to list and sample from all of its elements
Example Cluster SamplingA geologist, having collected a total of 600 soil samples, would like to revise his sampling methods for the possibility of contamination.
His first step would be to divide the samples into clusters. In this case, he can divide them according to the Mining Districts.
He must then randomly select clusters to sample from.Example Cluster Sampling ContdHaving selected his clusters, he can then use the soil samples within these clusters to conduct his exercise.
Advantages of Cluster SamplingCheap, easy to access data
Instead of having a sample scattered over the entire coverage area, the sample is more localized in relatively few clusters
Disadvantage of Cluster SamplingGenerally provides less precisionImportant NoteAlthough strata and clusters are very similar, they differ in the following ways:
All strata are represented in the sample; but only a subset of clusters are in the sample.
With stratified sampling, it is recommended that strata are internally homogenous
Custer Sampling yields the best results when clusters are internally heterogeneousSystematic SamplingThis method is appropriate for very large populations and gives a evenly spread across the population.
The population is listed/arranged according to some ordering scheme and then selecting elements at regular intervals through that ordered list.
Systematic SamplingSystematic sampling involves a random start and then proceeds with the selection of every nth (interval) element from then onwards.Systematic Sampling ContdN = size of population/size of sampling.
It is important that the starting point is not automatically the first on the list but a random element between the first and the nth element on the list.
This method is different from simple random sampling since every possible sample of the nth elements is not equally likely.Example Systematic SamplingA Mechanical Consultant Agency was hired to inspect the 10,000 caterpillar gasoline engines owned by MACORP Inc. If a systematic sample of 500 caterpillar gasoline engines were to be used to conduct the survey.
All engines would be assigned sequential numbers.
Example Systematic SamplingThe sampling interval (n) would be:
n = Population size / Sample sizen = 10,000/500 = 20
Note: that if n is not a whole number, it should be rounded to one.
Example Systematic SamplingThe starting point would be chosen by selecting a random number between one (1) and twenty (20). If this number was 7, then the 7th engine on the list of engines would be selected along with every 20th engine.
The sample of engines would be those corresponding to the engine numbers 7, 27, 47, .9927, 9947, 9967, and 9987.
Advantages of Systematic SamplingEasy to draw members of the sample
Distributes the sample more evenly over the populationDisadvantages of Systematic SamplingMay give a biased sample
A list may be needed to begin with if you wish to calculate the sample size and sample interval.Multi-Stage SamplingThis is a combination of two or more of the four (4) previous methods.
It is useful in very large research studies such as nationwide studies.
Multi-stage sampling, like cluster sampling, involves selecting a sample within each chosen cluster, rather than including all units in the cluster.
Therefore, multi-stage sampling can have at least two stages.Procedure in Multi-Stage SamplingThe first stage of multi-stage sampling is the construction of clusters.
The second stage is deciding what desirous elements with in the cluster is being analyze.
This selection of characteristics of elements within subsets of subsets is done until the final characteristic is achieved.Diagram
Example Multi-Stage Sampling In conducting multi-stage sampling, a total of 2,000 transformers can be divided into clusters according to their locations e.g. West Coast Demerara, East Coast Demerara, East Bank Demerara, etc.
Secondly, the clusters can then be further divided according to the various villages the transformers are located in.49Example Multi-Stage Sampling Contd The third stage includes analyzing based on their use e.g. residential, commercial, industrial, etc.
And, fourthly, individual houses, businesses and factories are selected from within the selected villages. This selection can continue until the desirous characteristic is achieved.
50Advantages of Multi-stage SamplingDoes not require a complete list of members in the target populationDisadvantages of Multi-stage SamplingLower accuracy due to higher sampling errorNon-probability Methods of Sampling:Quota Sampling
Convenience Sampling
Quota SamplingQuota sampling is widely used in market research where the population is divided into groups in terms of sex, age, income etc. The interviewer is told how many persons to interview within each specific group, but is given no specific instruction about how to locate them. This method is used in street interview surveys.Convenience SamplingConvenience sampling does not produce a representative sample of the population because people or items are only selected for a sample if they can be accessed easily and conveniently.
Example:The first ten bench marks.The closest dredges to the Mining Station
Errors in SamplingSampling error is any type of bias that is attributable to mistakes in either drawing a sample or determining the sample size.
Sampling Error is the difference between a sample mean (or proportion) and the population mean (or proportion).Reasons for Sampling ErrorsDifferent samples drawn from the same population can have different properties.
When you take a sample from a population, you only have a subset of the population, i.e. a piece of what youre trying to understand.SummaryConclusionFrom the presentation it can be concluded that sampling methods are very useful in statistical studies and gives fairly accurate results on the related study while being both time and cost efficient. ReferencesWikipedia. Sampling (Statistics). 2009. Retrieved on February 1st, 2015. .Answers.com. Sampling. 2009. Retrieved on February 3,2015. .http://stattrek.com/Lesson6/SRS.aspx - Retrieved February 2, 2015.http://stattrek.com/Lesson6/STR.aspx - Retrieved February 2, 2011.http://stattrek.com/Lesson3/SamplingTheory.aspx - Retrieved February 3, 2015.http://www.socialresearchmethods.net/tutorial/Mugo/tutorial.htm -Retrieved February 1, 2015
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